Modelling of complex corroding industrial systems is critical to effective inspection and maintenance for assurance of system integrity. Wall thickness and corrosion rate are modelled for multiple dependent corroding components, given observations of minimum wall thickness per component. At each inspection, partial observations of the system are considered. A Bayes linear approach is adopted simplifying parameter estimation and avoiding often unrealistic distributional assumptions. Key system variances are modelled, making exchangeability assumptions to facilitate analysis for sparse inspection time series. A utility-based criterion is used to assess quality of inspection design and aid decision making. The model is applied to inspection data from pipework networks on a full-scale offshore platform.